A damp washcloth is hung over the edge of a table todry. Thus, part (mass=m on )

Question

A damp washcloth is hung over the edge of a table todry. Thus, part (mass=mon) of the washcloth restson the table and part(mass=moff) does not. Thecoefficient of static friction between the table and the washclothis 0.40. Determine the maximum fraction[moff/(mon+moff)] that can hangover the edge without causing the whole washcloth to slide off thetable. answer: 0.29 A damp washcloth is hung over the edge of a table todry. Thus, part (mass=mon) of the washcloth restson the table and part(mass=moff) does not. Thecoefficient of static friction between the table and the washclothis 0.40. Determine the maximum fraction[moff/(mon+moff)] that can hangover the edge without causing the whole washcloth to slide off thetable. answer: 0.29

Explanation / Answer

A damp washcloth is hung over the edge of a table todry. Thus, part (mass=mon) of the washcloth restson the table and part(mass=moff) does not. Thecoefficient of static friction between the table and the washclothis 0.40. Determine the maximum fraction[moff/(mon+moff)] that can hangover the edge without causing the whole washcloth to slide off thetable. answer: 0.29

let the total length of the cloth be L
and part that overhands be l
now down ward pulling force=frictional force between the remainingpart and the table
let the total mass of the cloth be M and mass of unitlength=M/L
now according to above equilibrium
l*(M/L)*g=(L-l)(M/L)g
              =0.4(L-l)(M/L)g
calculating 1.4l=0.4L
l/L=0.2857=0.29

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